Olak

In this paper, we study the problem of the anchored k -core. Given a graph G , an integer k and a budget b , we aim to identify b vertices in G so that we can determine the largest induced subgraph J in which every vertex, except the b vertices, has at least k neighbors in J . This problem was introduced by Bhawalkar and Kleinberg e t al. in the context of user engagement in social networks, where a user may leave a community if he/she has less than k friends engaged. The problem has been shown to be NP-hard and inapproximable. A polynomial-time algorithm for graphs with bounded tree-width has been proposed. However, this assumption usually does not hold in real-life graphs, and their techniques cannot be extended to handle general graphs. Motivated by this, we propose an efficient algorithm, namely onion-layer based anchored k-core (OLAK), for the anchored k -core problem on large scale graphs. To facilitate computation of the anchored k -core, we design an onion layer structure, which is generated by a simple onion-peeling-like algorithm against a small set of vertices in the graph. We show that computation of the best anchor can simply be conducted upon the vertices on the onion layers , which significantly reduces the search space. Based on the well-organized layer structure, we develop efficient candidates exploration, early termination and pruning techniques to further speed up computation. Comprehensive experiments on 10 real-life graphs demonstrate the effectiveness and efficiency of our proposed methods.